In recent years, stress and anxiety have been identified as two of the leading causes of academic underachievement and dropout. However, there is little work on the detection of stress and anxiety in academic settings and/or its impact on the performance of undergraduate students. Moreover, there is a gap in the literature in terms of identifying any computing, information technologies, or technological platforms that help educational institutions to identify students with mental health problems. This paper aims to systematically review the literature to identify the advances, limitations, challenges, and possible lines of research for detecting academic stress and anxiety in the classroom. Forty-four recent articles on the topic of detecting stress and anxiety in academic settings were analyzed. The results show that the main tools used for detecting anxiety and stress are psychological instruments such as self-questionnaires. The second most used method is acquiring and analyzing biological signals and biomarkers using commercial measurement instruments. Data analysis is mainly performed using descriptive statistical tools and pattern recognition techniques. Specifically, physiological signals are combined with classification algorithms. The results of this method for detecting anxiety and academic stress in students are encouraging. Using physiological signals reduces some of the limitations of psychological instruments, such as response time and self-report bias. Finally, the main challenge in the detection of academic anxiety and stress is to bring detection systems into the classroom. Doing so, requires the use of non-invasive sensors and wearable systems to reduce the intrinsic stress caused by instrumentation.